Glass Volume Material with Caustics and Colored Shadow
You're getting a glow because you're adding two transparent BSDFs, so transmitted light is getting doubled. If you want transparent tint with the fake caustics, you would just multiply the transparent color and the fake caustics mask.

However, normally you wouldn't want to apply any color tint to the transparent BSDF, just the fake caustics. The volume absorption shader will take care of tinting the fake caustics. You can fix both of those node setups by just deleting the add shader and the transparent BSDF connected to it.

Adding color to any surface shader represents a color change that happens at the surface, while the interior is clear. This is usually not the case with glass unless the surface has been covered by a transparent paint. Normally the color is within the glass and the surface is clear, so all color should be in the volume shader.